Journal of East China Normal University(Natural Science) >

2015 , Vol. 2015 >Issue 1: 27 - 41

DOI: https://doi.org/10.3969/j.issn.1000-5641.2015.01.004

Article

Cells of the weighted Coxeter group (B3, ?)

  • MI Qian-Qian ,
  • SHI Jian-Yi
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Received date: 2013-12-01

  Online published: 2015-03-29

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Abstract

The affine Coxeter group ( e B3, S) can be realized as the fixed point set of the
affine Coxeter group ( e D4, eS) under a certain group automorphism α with α( eS) = eS. Let
e? be the length function of e D4. We gave an explicit description for all the left cells of the
weighted Coxeter group ( e B3, e?). Also§we showed that in the the weighted Coxeter groups
( e D4, e?) and ( e B3, e?), each left (respectively, two-sided) cell was left-connected (respectively,
two-sided-connected).

Key words： weighted Coxeter group; quasi-split case; cells; left-connectedness

Cite this article

MI Qian-Qian , SHI Jian-Yi . Cells of the weighted Coxeter group (B3, ?)[J]. Journal of East China Normal University(Natural Science), 2015 , 2015(1) : 27 -41 . DOI: 10.3969/j.issn.1000-5641.2015.01.004

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